SOLUTION: Dealing with contradiction: Show that for any positive integer a and any prime p, if p is divides a, then p does not divide a+1.

Question 32755: Dealing with contradiction: Show that for any positive integer a and any prime p, if p is divides a, then p does not divide a+1.
Answer by venugopalramana(3286) (Show Source): You can put this solution on YOUR website!
P|A...SO A=P*M....WHERE M IS AN INTEGER
FOR P TO DIVIDE A+1...
P|PM+1...IMPLIES
(PM+1)/P IS AN INTEGER...THAT IS M+(1/P)IS AN INTEGER...THAT IS 1/P IS
AN INTEGER...THIS IS NOT POSSIBLE AS 1 HAS NO DIVIDERS EXCEPT IT SELF
AND P BEING A PRIME NUMBER DIFFERENT FROM 1 CANNOT DIVIDE 1.
RELATED QUESTIONS
An integer n is called square-free if there does not exist a prime number p such that... (answered by richard1234)

Use the factor theorem to show that if 2^p - 1, where p does not equal 3, is a prime... (answered by Edwin McCravy)

Prove: if 4 divides mn, then m is even or n is even. i saw that this was p implies q... (answered by richard1234)

Prove that no rational number is equal to √p, where p is a prime number, using... (answered by ikleyn)

To show that is an irrational number unless n is a perfect square, explain how the... (answered by solver91311)

I need to prove: if a divides b then a divides bx for any integer... (answered by richard1234)

What is the smallest positive integer p for which 2^2p + 1 is not a prime... (answered by rapaljer)

Use the binomial theorem and mathematical induction to show the following. Let p be a... (answered by khwang)

For any positive integer p, let f(p) denote the largest prime factor of p.which of the... (answered by rothauserc)